1. Field of the Invention
The present invention relates to a method for selecting sample positions on a substrate a method for providing a representation of a model of properties of a substrate, a method of providing a representation of the variation of properties of a substrate across the substrate and a device manufacturing method.
2. Related Art
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., comprising part of, one, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In order to allow a number of patterned layers to be positioned on the substrate, it is desirable to accurately set the position of the substrate relative to the radiation beam and the patterning device. This may be performed by accurately positioning the substrate on a substrate table and positioning the substrate table relative to the radiation beam and the patterning device.
Alignment of the substrate may be performed. In one alignment system, a number of alignment marks on the substrate are measured to derive a coordinate system, which is compared to a modelled grid to derive the positions of features on the substrate. Clamping of the substrate on the substrate table, or wafer distortion occurring in non-lithography process steps, may cause distortion of the substrate, which can be monitored by comparison of the measurements to the grid. Models describing the wafer grid may be created which are used in exposing wafers so as to compensate for the distortions.
Measurements of the overlay, i.e., the alignment of successive layers formed on the substrate, may also be made using a modelled grid. Grid models describing the overlay error over the substrate with respect to the previous layer may be produced and used in a control loop to ensure lot to lot consistency.
In order to provide a useful model for substrate properties, such as the overlay error, across the substrate, a number of positions at which measurements may be made may be required. Accordingly, when a layout of a substrate, namely the arrangement of patterns to be formed on the substrate, is planned, a number of sample positions are provided. The requisite substrate property, such as the overlay error may be measured at each sample position or derived from measurements made at each sample position.
However, a finite amount of time is required to measure a desired property of the substrate at each sample position. Accordingly, although measuring the properties of the substrate at every sample position may provide a large amount of data for use in modeling the variation of the substrate property across the substrate, the amount of time taken to perform the measurements may be undesirable.
It has therefore previously been known to use a selection of the available sample positions, based on the intuition and/or experience of the user regarding which of the available sample positions should be used.